Unit circle

A circle of radius one, usually centered at the origin of a coordinate plane. Its points encode angles and trigonometric values through their coordinates.

Cartesian coordinate system: A system that locates points using signed distances from perpendicular axes. The circle is usually drawn in this coordinate system, with its center at the origin.
Sine: A trigonometric function that gives the vertical coordinate of a point on the unit circle. The point's height at angle θ is sin θ.
Trigonometric functions: Functions that relate angles to ratios or coordinates, including sine, cosine, and tangent. The unit circle provides a geometric definition of their values for all real angles.
Circle: The set of points in a plane at a fixed distance from a center. A unit circle is the special case whose fixed distance is one.
Euclidean distance: The straight-line distance between two points, calculated from their coordinate differences. Every point on the unit circle is exactly one unit from its center.
Cosine: A trigonometric function that gives the horizontal coordinate of a point on the unit circle. The point's horizontal position at angle θ is cos θ.
Periodic function: A function whose values repeat after a fixed nonzero interval. A full revolution returns to the same point, giving sine and cosine period 2π.
Unit sphere: The set of points at distance one from the origin in three-dimensional space. It generalizes the unit circle from a plane to three dimensions.
Angle: A measure of rotation or separation between two intersecting rays. An angle determines where a point lies as it moves around the circle.
Tangent: A trigonometric function equal to sine divided by cosine wherever cosine is nonzero. Unit-circle coordinates give tan θ as the ratio of vertical to horizontal position.

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